Unveiling real-time pulsation characteristics and programmable switching of 3D optical soliton molecules

Three-dimensional (3D) dissipative solitons, arising from the interplay of spatiotemporal nonlinear interactions, exhibit substantial similarities to other multi-dimensional physical phenomena. In particular, the investigation of 3D soliton molecules holds great potential for deciphering the underlying mechanisms of molecular complexity and addressing unresolved challenges in nonlinear systems. However, the pulsation of 3D soliton molecules, beyond stationary states, remains largely unexplored in the experiment. Here, we reveal the real-time pulsation characteristics and programmable switching of 3D soliton molecules, enabled by a single-shot multispeckle spectral-temporal measurement technique. Diverse dynamics of 3D molecules are captured, including the generation of period-doubling and beyond, desynchronization-synchronization transition, and controllable fast switching under programmable pump modulation. The mechanism of pulsation characteristics of the 3D soliton molecule is elucidated by numerical simulation. Further studies indicate the gain-induced nonlinear spatiotemporal coupling drives the 3D soliton molecule with frequency-locking in the spectral domain and noticeable mode dissipation in the spatial part, forming a unique dissipative soliton state. Our findings provide a new perspective for unveiling the complexity of 3D soliton molecules, and bring new insights into the underlying nonlinear physics of multi-dimensional lasers as well as a variety of applications.